How to achieve pressing against invisible wall effect facing camera? (animation)
This is not a simulation but a similar effect can be obtained very simply with a shrinkwrap modifier:



Set the modifier to "Project" and "Outside" (if orientation faces the model / normal of it pointing to the monkey).

Axis the one of the glass normal. Direction: positive. Cull face is not needed.

I've added a subdivison after it to curve a bit vertices that are stretched by the glass.